6 Answers
6

In general, we tend to use the as an article for nouns and proper nouns where it is clear from context that only one thing belongs to that description (or when we are talking about the archetypal thing of a set of things in the abstract). Otherwise we would normally use a to signify that we mean a single element out of a group of things that all fit the description.

General rules for articles

For example:

The President of the United States is Barack Obama.

There is only one sitting US President, so the is the correct article to use here, but...

President Obama is a Democratic President.

There is more than one President from the Democratic Party, so a fits better here.

The most populous country is China.

*We use the here because there is only one "most populous country"*.

The President lives in the White House

Although there are many houses that are white, and there are even several copies of the famous White House, the context here makes it pretty clear which one we're talking about, and there's no ambiguity. Similarly it is clear which President we are talking about from context, and there's only one that fits the context.

This isn't even limited to proper nouns:

I'm going to turn on the TV

Although there are many TVs in the world, it is clear from context which one I mean.

I am looking forward to the launch of the PlayStation 4

*The second the here is talking about the singular product called "PlayStation 4", of which there is one (even though there are many units that will be sold), and the first the refers to the singular event which is the launch of that product*.

I own a PlayStation 3

Since I own only one of many PlayStation3 units

Rules for omitting articles

Here are some rules of thumb that will help you get by.

Items with numerical count or position normally have articles omitted (more detail)

I came first in the pie-making contest!

(X) I came a first in the pie-making contest!

(X) I came the first in the pie-making contest!

Here are six apples.

(X) Here are a six apples.

(X) Here are the six apples.

Unless you are specifically referring to this group, which should be clear from context:

Here are the six apples [that we were talking about earlier].

2: Avoid putting adjectives on noun-phrases with omitted articles, but if you do prefix with an adjective, the article must be reintroduced:

Buckingham Palace is world-famous!

We visited the world-famous Buckingham Palace yesterday!

Except when talking about countries:

Join us on our exciting tour of historic China!

3: Never omit an article if the noun-phrase contains of:

The British Parliament sits in the Palace of Westminster.

The British parliament sits in Westminster Palace.

4: Always omit articles when talking about people by name.

(X) I love the Oprah Winfrey.

I love Oprah Winfrey.

But not, if the name of the individual is just part of a noun-phrase that isn't a person:

I love the Oprah Winfrey show

(X) I love Oprah Winfrey show

5: Omit articles when talking about companies by name or the buildings named after them.

She works at Microsoft.

(X) She works at a Microsoft.

(X) She works at the Microsoft.

When there are many places that share the same company name (e.g. McDonalds, Starbucks), then you can either omit the article, or use a. You can also always use the when talking about a specific place that is clear from context.

We'll meet at the top of Victoria Street and then we'll go to Brixton later.

The Great Lakes is a collection of lakes, so has an article.

But there are exceptions that must be learned by rote, such as

The International Criminal Court is based in the Hague.

I grew up in the Bronx.

7: We usually omit the article when talking about countries:

Some countries omit the, some don't. By default, the article is omitted, but it is reintroduced if:

The country name is derived from a plural:

The United States, the US (but not America), The United Kingdom, the UK (but not Great Britain, England etc), the USSR (but not Russia), The United Arab Emirates

The Azores, the Canaries, the Falklands, the Galapagos, the Bahamas, the Dao Yu Islands

The Philippines, the Netherlands.

The Russian Federation, The British Empire, The Roman Empire.

Remember: if the country is being given its full name including style of government, it regains an article by rule (3) above.

The People's Republic of China (but "I visited China")

The Islamic Republic of Iran (but "Iran is a beautiful country").

And there are a whole bunch of random exceptions:

The Vatican has an article, but Vatican City doesn't.

The Gambia uses an article, although it is sometimes used without one.

The Democratic Republic of the Congo is often (unofficially) called "The Congo".

Before 1991, Ukraine was referred to as the Ukraine (short for "the Ukrainian Soviet Socialist Republic"), but now has no article. In the mid 20th Century, "The Argentine" became known as Argentina.

We used to say "The Lebanon" (from the literal translation of HaLevanon), but now "Lebanon" is normally given with no article.

8: Some nouns are used without articles to indicate that they are being used in idiomatic form:

She went to bed (means she went to her bed in order to sleep)

She went to work (she went to her workplace to perform her job).

She went to school/university/college (means she attended her school. Also variants such as Summer school and Sunday school can be used this way.)

She went to church (means she attended church. Other religious places cannot be used this way. Articles are normally used for "He went to the temple/cathedral/mosque/synagogue etc")

She went to war (means she went to fight as part of the military abroad).

She went to prison/jail (means she was convicted of a crime, and was incarcerated).

She went to hospital (she was admitted to hospital. esp. British English).

She went to court (she was brought before a judicial court, either as the plaintiff or as the defendant, or possibly as a lawyer or judge presiding).

These nouns can be used with articles when the idiomatic form is not wanted and we want to refer to the noun in it's "ordinary" form:

The bed is broken.

The church is next to the synagogue.

The war in Iraq started in 2003.

I went to the prison in order to better understand the psyche of the inmates. (as opposed to I went to prison in order to..., which would imply that the speaker was incarcerated, rather than just visited).

I went to the hospital on Tuesday to pick up Auntie May.

These forms just need to be learnt.

9: Most names which are constructed from a possessive form of a person, city, county or suburb drop the article.

We visited Beeston Castle the other day!

Nelson's Column is 169 ft 3 in tall!

Queen Elizabeth I is buried at Westminster Abbey.

Kensington Gardens are very famous.

Seattle Tower is more commonly known as "The Space Needle".

Munich Cathedral is very impressive.

I'm writing a letter to Westminster City Council.

Sydney Opera house is amazing!

We visited St. Paul's Cathedral on Tuesday.

But

The Science Museum and the Natural History Museum are right next to each other.

The Tate Modern is quite expensive, but well worth the trip.

The British Library is free.

10: Nouns which are personal qualities are usually given with no article (see StoneyB's answer here)

He certainly has talent. (He is talented)

Nobody denies her courage. (She is courageous)

Sartorius lacks generosity. (Sartorius is not generous)

11: Most other nouns take an article, and the ones that don't tend to inconsistently have their articles used or not used by native speakers, so don't worry too much about them, and learn them by rote as and when they come up.

For example:

The Wikipedia article on Hagia Sophia uses the article "the" for Hagia Sophia 23 times but omits it 22 times.

"Taj Mahal" normally takes an article, but the official website uses both forms.

The Washington Monument / The Lincoln Memorial normally (but do not always) take articles.

on that last point, a fairly good rule of thumb is that you use an article for a country name if that name includes a common noun that means a particular type of country/government/land mass, e.g. "the People's Republic of China", "the Union of Soviet Socialist Republics", "the United Arab Emirates", "the Turks and Caicos Islands", etc. (China is a bit wierd, though, as the short form of it's name drops the article, but probably easier to memorize the exceptions.)
– KutuluMikeSep 18 '13 at 14:38

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Additional note on the last one: "the Ukraine" used to be common, so you'll probably hear it on occasion, but as @MichaelEdenfield notes, the correct usage has changed.
– IzkataSep 18 '13 at 15:07

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In the OPs question he states the rule he was taught as "we don't use 'the' except for river names, newspaper names, etc" The big catch there is the "etc". The list of exactly when we use "the" and when we don't is not -- to my mind at least -- particularly consistent or obvious. It's just a set of conventions that you have to learn. Like why do we use "the" with names of rivers but not with names of lakes? I have no idea. That's just the convention.
– JaySep 18 '13 at 20:21

Ha ha! 20 edits! That's what you get for trying to write a complete treatise on the definite article. :^) This is a noble effort, though.
– J.R.♦Sep 19 '13 at 12:51

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Great Lakes are, not *Great Lakes is, surely. Fun fact: in the US there's geographical variation as to whether numbered roads take an article. Where I grew up (near the Great Lakes, incidentally), we'd say "driving on 280" or "take 355 north", but in Southern California people tend to say "the 60" or "take the 101 north".
– snailboat♦Sep 22 '13 at 7:04

Sometimes there is no fixed rule. The Purdue OWL gives some guidelines about "Geographical" uses, but it doesn't say much about buildings and landmarks. However, the White House isn't the only building that uses the definite article; that practice seems to be rather common:

Don't get caught up on the fact that "White House" could be read as a description, that is, a house that is white. There are many words and phrases out there that have a general meaning, but that become proper names in one particular context. When we say "The president lives in the White House", we don't mean simply that he lives in some house that happens to be white, but rather that he lives in a particular building which is called by the name "White House". Similarly, if I say, "General Jones works in the Pentagon", I am not using the word "pentagon" in its general meaning as a geometrical shape, but rather to a particular building that is called by this name. I live near the Great Lakes. I'm sure there are many other lakes in the world that are great, but these particular lakes are named "the Great Lakes". This isn't limited to place names. There might be many companies in Britain that do something related to broadcasting, but if I say "the British Broadcasting Company" I am referring to one particular company that goes by that name. Etc.

As I understand it, there are two possible rules that can lead to this "the" before the phrase "White House".

When the speaker/writer believes that the hearer/reader knows exactly what he is referring to, e.g: The White House is white. Both the speaker and the reader know exactly which "White House" the speaker is talking about.

When there is only one thing referred by "the". Such as The Earth, The Sun, The 44th president of America and by extension The White House. I'm guessing there is only one White House on this planet.

On second thought, I think you logic is not too foolproof. E.g., there is only one Mount Everest, but we don't use 'the' with it.
– RamitSep 18 '13 at 10:14

Yeah, cause Mount Everest is a single mountain, which English rule doesn't put any article in front of it. But if that is a mountain range like himalyas, that will be the Himalyas. For more proof you can take a look at this: more info, straightly on point 5.
– SafiraSep 18 '13 at 10:23

I am actually looking for the comparison b/w White House and Mount Everest. Both are unique on the earth (aren't they), yet one uses a determiner and one doesn't.
– RamitSep 18 '13 at 10:37

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It is not true that there is just a White House: In Moscow, there is a government building that is called White House.
– kiamlalunoSep 18 '13 at 12:37

That's a very nice logic. Does it work in reverse as well? Like, Himalyas is not derived either, still it uses an article.
– RamitSep 18 '13 at 18:50

There is another usage worth mentioning here. Sometimes we use "the" not because there is only one thing we could be talking about, but because we want to emphasize that the one we're talking about is the one that is familiar to everyone.

For example, if I'm introduced to somebody named Brian Wilson, I might ask, "Are you the Brian Wilson?", with emphasis on the. I'm asking if he is indeed the singer from the Beach Boys, and not some other not-so-famous person who is also named Brian Wilson.

The White House is not the most popular white house; it is just a building that is called White House. There is the White House in the USA, and there is the White House in Moscow; even in the USA, there is more than one building called White House.
– kiamlalunoSep 19 '13 at 12:31

@kiamlaluno - Spot on. If they had decided to name the White House "the Presidential Manor" instead, we'd still call it the Presidential Manor. Still, the Photon makes an interesting point about the Brian Wilson.
– J.R.♦Sep 19 '13 at 12:47